This is not about reducing noise it is about fixing aberration and distortion.

So it even works on noisy images where you get a better quality image of the (still) noisy image.

They never mention that they extract details that aren't there. They just present details in a way that humans perceive as "sharper images".

You note about scanners is interesting. There once was a project that converted scanned disk record into MP3s. You had to scan the disk several times because of the scanners aberration (http://www.cs.huji.ac.il/~springer/DigitalNeedle/index.html).